Write a rule for the function

[CandiceBFureal]

We have a table with input and output numbers.
We need to find the rule for the function.
Input is on the top of the table
Output is on the bottom of the table
1 3 1 -3
1 4 1 5
There is an error on the pairing and we know this is one of the 1's as there cannot be two X's the same.
We dont however know which pair is the incorrect one.
We do know that the (3,4) and the (-3,5) are correct.

We have tried to square them. that will eliviate the neg but cant get the output to be one digit off.
for ex: X(squared) -5= Y doesnt work. It works for the first set (3,4) but not the second set.

We have tried mutliplying by 1/3 or 1/4--- 1/3 doest work b/c it cancels it out and still cant get a one digit difference. in the output.

I feel we have over thought this for too long.
Any help?
Any suggestion in any direction would be very grateful.

 

[mmm4444bot]

We need to find the rule for the function.
Input is on the top of the table
Output is on the bottom of the table

1 3 1 -3
1 4 1 5

There is an error on the pairing and we know this is one of the 1's as there cannot be two X's the same.

We dont however know which pair is the incorrect one.

Huh? Both pairs are the same: (1, 1) and (1, 1).

Where is the error?


Any suggestion in any direction would be very grateful.

I found a quadratic function that passes through the three given points.

Do you know how to solve a system of three equations?

A quadratic function has the form:

y = Ax^2 + Bx + C

If you substitute the coordinates of a point into this form, you end up with an equation in A,B,C.

EG: Using the point (3, 4) leads to the equation 4 = 9A + 3B + C.

You have three points, so you can get three equations. Solve this system of three equations for the parameters A,B,C.

Use these values of A,B,C to write the function rule as y = Ax^2 + Bx + C.

 

[CandiceBFureal]

MMM
Thank you for helping.
I didn’t explain myself very well.

We are learning Writing a function rule
For example:

Input	3	6	7	10
Output	15	30	35	50

The Function rule would be y=5x


The Function consists of a set of domains (inputs) and the range (Outputs)
Outputs cannot be paired with the same input. In otherwords in the table the input must be different numbers.

In our problem we have the same digit input (#1) therefore one of these are incorrect.

Input	1	3	1	-3
Output	-1	4	1	5

So in order to find the Function rule we are limited to what we know to be true.
Which is

Input	3	-3
Output	4	5

The question is what is the function rule to this?

This is just 9^th grade math, I really feel im over looking a very easy solution. But my mind is mush

 

[wjm11]

In our problem we have the same digit input (#1) therefore one of these are incorrect.

How do you know that either one of the data points (1,1), (1,-1) is correct? Was that in the problem statement? What EXACTLY was the problem statement?

If neither (1,1) nor (1,-1) is a reliable value, you only have two data points: (3,4) and (-3,5). With only two data points, you could write a linear equation that passes through those points. Do you know how to write the equation for a line if you are given two points on that line?

On the other hand, if one of the points (1,1), (1,-1) IS an actual data point, you now have three know points, and they are not colinear (i.e., they are not on the same line). In that case, you could (as MMM pointed out) find two quadratic equations that would fit the two, 3-point data sets.

 

[mmm4444bot]

I didn’t explain myself very well.

No, the issue is that you confused me by making a typographical error with the table in your original post. I told you that both points were (1,1), and I specifically asked you, "Where is the error?" Do you not see it? You left off the negative sign in front of -1. Now that you've told us that one of those two points is actually (1, -1), we know that there is no possible function whose graph goes through those four points.



Outputs cannot be paired with the same input.

Yes they can, if these outputs are always the same number. That's the definition of a function; no matter how many times you input some fixed number, you always get the same output.

You left off the word "different", above.

Different outputs cannot be paired with the same input.

I agree with wjm11. If we're given only two points, then the function is linear:

y = m*x + b


As an aside, if the domain of the function were {-3, 3} and the range were {4, 5}, then the function would be discrete (that is, the graph would consist of only two points), and there would be no rule.

 

[Deleted member 4993]

We have a table with input and output numbers.
We need to find the rule for the function.
Input is on the top of the table
Output is on the bottom of the table
1 3 1 -3
1 4 1 5
There is an error on the pairing and we know this is one of the 1's as there cannot be two X's the same.
We dont however know which pair is the incorrect one.
We do know that the (3,4) and the (-3,5) are correct.

We have tried to square them. that will eliviate the neg but cant get the output to be one digit off.
for ex: X(squared) -5= Y doesnt work. It works for the first set (3,4) but not the second set.

We have tried mutliplying by 1/3 or 1/4--- 1/3 doest work b/c it cancels it out and still cant get a one digit difference. in the output.

I feel we have over thought this for too long.
Any help?
Any suggestion in any direction would be very grateful.

Here you have (1,1) and (1,1) as your data. As those are repeated points, there should be no confusion.

 

[mmm4444bot]

Subhotosh, the original table contains a typographical error. This error was subsequently corrected, as seen in CandicesBFureal's second post (partial quote below).

Input	1	3	1	-3
Output	-1	4	1	5